10-160*x-80*x^2=0

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Solution for 10-160*x-80*x^2=0 equation: 


Simplifying
10 + -160x + -80x2 = 0

Solving
10 + -160x + -80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -16x + -8x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(1 + -16x + -8x2)' equal to zero and attempt to solve:

Simplifying
1 + -16x + -8x2 = 0

Solving
1 + -16x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.125 + 2x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 2x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 2x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 2x + x2 = 0 + 0.125
2x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
2x + x2 = 0.125

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.125 + 1

Reorder the terms:
1 + 2x + x2 = 0.125 + 1

Combine like terms: 0.125 + 1 = 1.125
1 + 2x + x2 = 1.125

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(x + 1) equal to 1.060660172 and -1.060660172.


Subproblem 1
x + 1 = 1.060660172

Simplifying
x + 1 = 1.060660172

Reorder the terms:
1 + x = 1.060660172

Solving
1 + x = 1.060660172

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 1.060660172 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.060660172 + -1
x = 1.060660172 + -1

Combine like terms: 1.060660172 + -1 = 0.060660172
x = 0.060660172

Simplifying
x = 0.060660172


Subproblem 2
x + 1 = -1.060660172

Simplifying
x + 1 = -1.060660172

Reorder the terms:
1 + x = -1.060660172

Solving
1 + x = -1.060660172

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = -1.060660172 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.060660172 + -1
x = -1.060660172 + -1

Combine like terms: -1.060660172 + -1 = -2.060660172
x = -2.060660172

Simplifying
x = -2.060660172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.060660172, -2.060660172}
Solution
x = {0.060660172, -2.060660172}

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